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Journal of Molecular Spectroscopy198,110–114 (1999)Article ID jmsp.1999.7941, available online at http://www.idealibrary.com on

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Rovibrational Constants for the n6 and 2n9 Bands of HCOODby Fourier Transform Infrared Spectroscopy

T. L. Tan,* K. L. Goh,† P. P. Ong,† and H. H. Teo†

*Division of Physics, School of Science, Nanyang Technological University, National Institute of Education, 469, Bukit Timah Road, Singapore6,Singapore; and†Department of Physics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, Sin

Received April 19, 1999; in revised form July 20, 1999

The Fourier transform infrared spectrum of then6 and 2n9 bands of deuterated formic acid (HCOOD) was recorded with anapodized resolution of 0.004 cm21 in the frequency range of 930–1040 cm21. These two bands with band centers 40 cm21 apartwere mutually coupled by Coriolis and Fermi interactions. By fitting a total of 1076 infrared transitions of bothn6 and 2n9 witha standard deviation of 0.00075 cm21 using a Watson’sA-reduced Hamiltonian in theI r representation with the inclusion ofc-type Coriolis and a Fermi-resonance term, two sets of rovibrational constants forv6 5 1, andv9 5 2 states were derived forthe first time. Bothn6 and 2n9 bands areA type with band centers at 972.85206 0.0001 and 1011.67666 0.0001 cm21,respectively. © 1999 Academic Press

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INTRODUCTION

The vibrational bands of normal and isotopically substitormic acid, including the D,18O, 13C species, were assignededington (1) from low-resolution infrared spectra. Spectral dn formic acid (HCOOH) is applicable to the field of radioasomical studies as it was the first organic acid detected intellar space. It proved to be a rich source of far-infraredmission when pumped with the CO2 laser (2, 3). So far a numbef microwave, low-, and high-resolution infrared measurem4–18) were made on various bands of HCOOH, DCOO

13COOH, HCOOD, and DCOOD. In particular, high-resoluttudies for HCOOD were limited to then3 band (12, 18), then5

and (14), and then7 andn9 bands (15).In the present experimental work, we report for the first t

he results of the analysis of then6 and 2n9 bands of HCOODhich was measured in 930–1040 cm21 with an apodize

esolution of 0.004 cm21. The ground state constants where used in our nonlinear fit were derived from microw

ransitions (4) and the ground state combination differencehe n5 band of HCOOD (14). These constants representost accurate values to date.In the analysis of the rotational structure,n6 and the nearb

n9 band are found to be mutually coupled byc-type Coriolisnd Fermi-resonance terms. A total of 1076 infrared transi

nclusive of about 350 perturbed transitions were fitted simaneously to give an accurate set of rotational and alluartic centrifugal distortion constants for thev6 5 1 andv9 5states with a rms uncertainty of 0.00075 cm21. An analysis o

Supplementary data for this article is available on the journal homehttp://www.academicpress.com/jms) and as part of the Ohioniversity Molecular Spectroscopy Archives (http://msa.lib.ohio-statesa/jmsa_99.htm).

110022-2852/99 $30.00opyright © 1999 by Academic Pressll rights of reproduction in any form reserved.

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he Coriolis and Fermi interactions betweenn6 and 2n9 transi-ions givec-type Coriolis and Fermi-resonance constants.

EXPERIMENTAL DETAILS

Samples of HCOOD used in these measurements werehased from Cambridge Isotope Laboratories (Massachuhe sample consisted of a 95% by weight solution of HCOO2O, with a HCOOD chemical purity better than 98%. Materhich came into contact with HCOOD during the experimere Pyrex glass, Viton O-rings, perfluorinated grease, and

ess steel. They proved to be corrosion-resistant. The singleell with an absorption path length of 20 cm was fitted with Zindows. The KBr windows were found to be inert to HCOOuring the recording of the spectra, the HCOOD vaporhielded from ambient light to prevent photodecomposition.mbient temperature was 296 K.A Bomem DA3.002 Fourier transform spectrophotomete

he National University of Singapore was used to obtainpectra. An unapodized resolution of 0.0024 cm21 was usedhe vapor pressure was measured with a capacitance prauge designed for high corrosion-resistance. Due to the

ntensity of both spectra, a substantial pressure of 2.33as introduced into the sample cell in order to obtain speood enough for a rovibrational analysis.A KBr beamsplitter, a globar infrared source, a high-se

ivity liquid-nitrogen-cooled Hg–Cd–Te detector, and a loass band filter (0–1500 cm21) were used. To obtain a reasobly high signal-to-noise ratio level, six runs of 50 scans eere co-added to obtain the final sample spectrum. Thecanning time was about 28 h. A fresh sample of HCOapor was introduced into the absorption cell for each rupectrum of the evacuated absorption cell was recorded wesolution of 0.1 cm21 and transformed at 0.0024 cm21 with

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111THE n6 AND 2n9 BANDS OF HCOOD

ero-filling in order to obtain a background spectrum. Tpectrum was ratioed with the sample spectrum to obtaransmittance spectrum.

The spectrum was calibrated using the line frequencieH3 in the region 921–1035 cm21, given in Guelachvili anao (19). The NH3 lines were measured in a separate spec

ecorded immediately before the HCOOD spectrum wasorded. Corrections of about 0.00062–0.00069 cm21 were re-uired to bring the observed wavenumbers into agreemen

FIG. 1. Energy levels of the vibrational modes and symmetry typeCOOD. (“Dark states” are characterized by dotted lines.)

FIG. 2. A survey spectrum of then6 and 2n9 bands of HCOOD.

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he calibrated frequencies. The absolute accuracy of theration is estimated to be60.0002 cm21. However, the meaured frequency values are estimated to be accurate to60.0004m21 because of small systematic errors in the experime

ANALYSIS AND RESULTS

HCOOD is a near-prolate slightly asymmetric top (k 50.94) molecule withCs symmetry. It has nine fundamen

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FIG. 3. Detail of then6 P-branch region for HCOOD with assignments0 5 7 cluster.

FIG. 4. Detail of the 2n9 R-branch region for HCOOD with assignmef J0 5 5 cluster.

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112 TAN ET AL.

ands of which seven are in-plane and two are out-of-pibrations. Then6 band, which is a COD bend (1), and the 2n9

and are both in-plane and therefore should be assign

FIG. 5. (a) Deviations (obs.2 calc.) in cm21 for the perturbed levels phe perturbed levels plotted as functions of upper stateJ for 2n9.

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ybrid A- and B-type bands. The bands were analyzed torimarily A type. The energy levels of these nine bands,7 1 n9, and 2n9 and their corresponding symmetries,

d as functions of upper stateJ for n6. (b) Deviations (obs.2 calc.) in cm21 for

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FIG. 6. (a) Deviations (obs.2 calc.) in cm21 after the final fit plotted as functions ofKa for n6. (b) Deviations (obs.2 calc.) in cm21 after the final fit plotteds functions ofKa for 2n9.

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113THE n6 AND 2n9 BANDS OF HCOOD

llustrated in Fig. 1. Then6, 2n9, n8, andn7 1 n9 bands covespectral range of 930–1080 cm21. Figure 2 shows a surve

pectrum for the two bands, in the 950–1030 cm21 region. Theresence of prominent strong centralQ branch is characteristf A-type bands. Both bands are found to be generally qeak in intensity despite a high pressure used duringxperiments. Purelya-type transitions were found asb-type

ransitions were probably too weak to be observed foreasured bands.In the initial assignment of lowJ values of the two band

luster patterns separated by 0.72 cm21 (5B 1 C) werebvious. AsJ values get higher, the clusters widen and o

ap. Figure 3 shows the details of theJ0 5 7 cluster in thePranch ofn6. A large asymmetry splitting is observed asK 0a 5and 2 transitions while the rest are not split. Asymm

plittings are also observed forK 0a 5 1 and 2 transitions in th0 5 5 cluster of theR branch of 2n9, as shown in Fig. 4. It iound that asJ0 values increase for each cluster, asymmplitting occurs for even higherK 0a values.During our analysis, we found that the transitions for b

ands deviate quite badly due to their mutual interac

TABLE 1Rovibrational and Coupling Constants (cm21) for the vv6 5 1

and vv9 5 2 States of HCOOD (A-Reduction of the Ir

Representation)

a The ground state constants were derived from microwave transitioRef. (4) and ground state combination differences of Ref. (14).

b The uncertainty in the last digits (twice the estimated standard errogiven in parentheses.

c The values in square brackets were fixed to the ground state valued All rotational transitions were taken from Ref. (4).e For the ground state the number of infrared transitions is actually

number of combination differences used in the fit.

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erturbations of particular noticeability are theKa 5 4, 5, 6,nd 7 levels ofn6 and theKa 5 2, 3, and 4 levels of 2n9. Due

o the high deviations shown in Figs. 5a and 5b, we havnclude perturbation terms in order to fit both bands accuraowever, as shown in Fig. 1, 2n9 is not the only perturbinand ofn6; other bands which interfere withn6 and 2n9 are the8 band at 1035 cm21 and possibly the “dark” bandn7 1 n9

ituated at about 1063 cm21. In our spectrum, then8 band is nobserved because of its weak intensity. Perturbations ofn6 with8 affects theKa $ 8 levels of n6. As a result, due to thxcessive perturbations, we have excluded these levelsur fit in order to get better accuracy in our analysis.Accurate rovibrational ground states derived from miave transitions (4) and the ground state combination diffnces ofn5 band have made the preliminary assignments o6 spectrum straightforward. The usual iterative procetarting from low J and Ka values was employed for thonlinear fit. Eventually, about 453a-type transitions ofn6

ere assigned and fitted with a rms uncertainty of 0.000m21. Since this uncertainty value is comparable to the mured accuracy (0.0004 cm21) of each frequency line, it can bssumed that these transitions are not perturbed. In the nar fit, a Watson’sA-reduced Hamiltonian in theI r represen

ation was applied (20). In the nonlinear least-squares fit, enfrared transition was given an uncertainty of 0.0005 cm21. Inhe fitting process, transitions starting fromJ9 5 17 for K 0a 5

were found to be displaced as high as 0.07 cm21 symmetri-ally for both P and R branches. These deviations are illrated in Fig. 5a. Similarly, large deviations of observed waumber for n6 from corresponding calculated values w

ound for K 0a 5 4, 6, and 7. For 2n9, the deviations occur ihe opposite direction forJ9 5 9–22 andK 0a 5 2–4, asshownn Fig. 5b. A total of about 350 transitions for bothn6 and 2n9

ere found to be perturbed.The perturbed transitions observed during the fit can

ttributed to thec-axis Coriolis resonance and Fermi resonaetweenn6 and 2n9. Finally, a total of 697 infrared transitiof n6 and 379 transitions of 2n9 inclusive of about 350 pe

urbed transitions were finally assigned and fitted usinatson’sA-reduced Hamiltonian in theI r representation wit

he inclusion ofc-axis Coriolis and Fermi resonance couplerms. Thec-Coriolis couplings and Fermi resonance betwhe n6 and 2n9 levels are described using the following malements:

2n9, J, K 6 1uHun6, J, K&

5 6j c~1/ 2!@ J~ J 1 1! 2 K~K 6 1!# 1/ 2

^2n9, J, KuHun6, J, K& 5 WK2.

The derived rovibrational constants along with theiristical errors are shown in Table 1. Rotational and alluartic centrifugal distortion constants forn6 and 2n9 were

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114 TAN ET AL.

ccurately determined. The band centers forn6 and 2n9 wereound to be 972.8519576 0.000095 and 1011.6766476.000119 cm21, respectively. The sextic distortion constaf n6 and 2n9 which could not be determined accuratelyur fit were fixed at the ground state constants. In our fi

he upper states, the ground state constants were fixedhe latest available accurate values derived from microwransitions (4) and ground state combination differences5 of HCOOD (18).In our present work, we analyzed 1076a-type transitions o

othn6 and 2n9 covering the whole spectral range of 930–1m21. Thea-type transitions fromJ9 5 1–47 forn6 andJ9 5–23 for 2n9 were assigned and fitted. A rms deviation.00075 cm21 for 1076 transitions was achieved.Tables 2a and 2b, available as supplementary data, giv

ssignments of the perturbed transitions along with their dtions before (Dev1) and after (Dev2) the simultaneous fitn6

nd 2n9. As shown in Tables 2a and 2b, a large proportiohe perturbations’ deviations were reduced by more thanhis can be explained in terms of a considerable amouavefunction mixing ofn6 and 2n9 which resulted in therivations ofc-type Coriolis and Fermi-resonance interaconstants. The observed2 calculated residues obtained ahe simultaneous fit ofn6 and 2n9 which include the Coriolind Fermi-resonance terms in the perturbed region are pgainstKa as shown in Figs. 6a and 6b, respectively.pproximate symmetric distribution about the zero line iates that the behavior of the residues could be regardandom in nature in our experiments.

Hence, from our rovibrational analysis of the Coriolis aermi-resonance interaction betweenn6 and 2n9 bands oCOOD, thev6 5 1 andv9 5 2 constants up to quartic termnd c-Coriolis coupling and Fermi resonance constants w

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erived. They represent new accurate values for then6 and 2n9

ands of HCOOD.

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